Preliminary remarks on option pricing and dynamic hedging

Michel Fliess and Cédric Join ()
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Michel Fliess: LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Cédric Join: ALIEN - Algebra for Digital Identification and Estimation - Centre Inria de l'Université de Lille - Inria - Institut National de Recherche en Informatique et en Automatique - Centre Inria de Saclay - Inria - Institut National de Recherche en Informatique et en Automatique - Centrale Lille - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, CRAN - Centre de Recherche en Automatique de Nancy - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique

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Abstract: An elementary arbitrage principle and the existence of trends in financial time series, which is based on a theorem published in 1995 by P. Cartier and Y. Perrin, lead to a new understanding of option pricing and dynamic hedging. Intricate problems related to violent behaviors of the underlying, like the existence of jumps, become then quite straightforward by incorporating them into the trends. Several convincing computer experiments are reported.

Keywords: Quantitative finance; option pricing; European option; dynamic hedging; replication; arbitrage; time series; trends; volatility; abrupt changes; model-free control; nonstandard analysis; nonstandard analysis. (search for similar items in EconPapers)
Date: 2012-08-29
New Economics Papers: this item is included in nep-fmk
Note: View the original document on HAL open archive server: https://polytechnique.hal.science/hal-00705373v1
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Citations: View citations in EconPapers (4)

Published in 1st International Conference on Systems and Computer Science, Aug 2012, Villeneuve d'Ascq, France. pp.CDROM

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